Math Essentials, Middle School Level: Lessons and Activities for Test Preparation
October 2004, Jossey-Bass
Notes to the Teacher.
Section 1: Number, Operation, and Quantitative Reasoning.
1. Compare and order fractions, decimals (including tenths and hundredths), and percents, and find their approximate locations on a number line.
2. Multiply decimals to solve word problems.
3. Divide decimals to solve word problems.
4. Estimate solutions to multistepped word problems by rounding with decimals.
5. Add fractions or mixed numbers to solve word problems.
6. Subtract fractions or mixed numbers to solve word problems.
7. Divide fractions or mixed numbers to solve word problems.
8. Multiply fractions or mixed numbers to solve word problems.
9. Develop and apply scientific notation to solve word problems.
Section 2: Proportional and Algebraic Reasoning.
1. Apply ratios in proportional relationships involving unit rates, scale factors, probabilities, or percents.
2. Add integers to solve word problems.
3. Subtract integers to solve word problems.
4. Multiply and divide integers to solve word problems.
5. Model situations with linear equations of the form: aX + b = c, where a, b, and c are integers or decimals and X is an integer.
6. Identify linear and nonlinear functions and contrast their properties using tables, graphs, or equations.
Section 3: Geometry, Spatial Reasoning, and Measurement.
1. Sketch side views (orthogonal views) of solids and identify different perspectives of solids that satisfy the side views.
2. Identify or graph reflections (flips), rotations (turns), and translations (slides) on a coordinate plane.
3. Use dilations to generate similar two-dimensional shapes, and compare their side lengths, angles, and perimeters; find missing measurements using proportional relationships.
4. Model and apply the Pythagorean theorem to solve real-life problems.
5. Generate the formulas for the circumference and the area of a circle; apply the formulas to solve word problems.
6. Generate and apply the area formula for a parallelogram (including rectangles); extend to the area of a triangle.
7. Generate and apply the area formula for a trapezoid.
8. Apply nets and concrete models to find total or partial surface areas of prisms and cylinders.
9. Find the volume of a right rectangular prism, or find a missing dimension of the prism; find the new volume when the dimensions of a prism are changed proportionally.
Section 4: Graphing, Statistics, and Probability.
1. Locate and name points using ordered pairs of rational numbers or integers on a Cartesian coordinate plane.
2. Construct and interpret circle graphs.
3. Compare different numerical or graphical models for the same data, including histograms, circle graphs, stem-and-leaf plots, box plots, and scatter plots; compare two sets of data by comparing their graphs of similar type.
4. Find the mean of a given set of data, using different representations such as tables or bar graphs.
5. Find the probability of a simple event and its complement.
6. Find the probability of a compound event (dependent or independent).
--Ernest Oluwole Pratt, assistant professor, department of education, Mount Union College, Alliance, Ohio
"Middle school math teachers will want to take this book home with them every night! It addresses key middle school topics and provides easy-to-use activities which not only support the conceptual understanding of the topics but include links to their assessment."
--Francis (Skip) Fennell, professor of education, McDaniel College, Westminister, Maryland, former NCTM board member, and author, Principles and Standards for School Mathematics